Question

use technology to find points and graph the line $6x - 5y = 10$, following the instructions below.
done plotting points
plot at least two points that fit on the axes below. click a point to delete it.

Explanation:

Step1: Find x-intercept (y=0)

Set \( y = 0 \) in \( 6x - 5y = 10 \).
\( 6x - 5(0) = 10 \)
\( 6x = 10 \)
\( x = \frac{10}{6} = \frac{5}{3} \approx 1.67 \). Wait, better to find integer points. Let's try \( x = 0 \) for y-intercept.

Step2: Find y-intercept (x=0)

Set \( x = 0 \) in \( 6x - 5y = 10 \).
\( 6(0) - 5y = 10 \)
\( -5y = 10 \)
\( y = -2 \). So point (0, -2).

Step3: Find another point (x=5)

Set \( x = 5 \): \( 6(5) - 5y = 10 \)
\( 30 - 5y = 10 \)
\( -5y = -20 \)
\( y = 4 \). So point (5, 4).

Step4: Verify points

For (0, -2): \( 6(0) - 5(-2) = 10 \), \( 10 = 10 \) (valid).
For (5, 4): \( 6(5) - 5(4) = 30 - 20 = 10 \) (valid).

To graph \( 6x - 5y = 10 \), plot points like \((0, -2)\) and \((5, 4)\) (or others like \((\frac{5}{3}, 0)\) for x-intercept). Connect the points to draw the line.

Answer:

Two valid points are \((0, -2)\) and \((5, 4)\) (plot these on the axes to graph the line).